You can easily replicate this clock as I have included the logic diagram as well as a map of the actual ICs I used with their pin numbers and inputs labeled. The displays on the IC map are dual 7-segment common cathode displays. The software I used to create the schematics is LogicWorks 4.1.
Not included in the schematic is a 32KHz Crystal Oscillator (digikey.com part # DS32KHZ/DIP-ND) which is divided down to 1Hz using a 14-bit counter and a JK flip-flop in toggle mode. That signal is then fed to the first counter in the sequence which is used for the seconds portion of the clock. The switches used for the time set are SPDT momentary push buttons. When pressed and held, the 1Hz signal is forwarded to the targeted bit, which makes it temporarily count at a 1 second rate. The button is then released when it reaches the desired value. The bright blue LEDs seen inside the clock can be turned on or off (they can be slightly obnoxious when left on at night) with a basic on/off toggle switch that's on the back of the clock among the time set buttons. All other non-circuit related hardware, wood, etc. was purchased at Home Depot.